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On the Definition of the Strategic Stability of Equilibria

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  • Hillas, John

Abstract

A new definition of strategic stability is shown to satisfy all of the requirements given by Elon Kohlberg and Jean-Francois Mertens (1986). The definition follows the general form of the original definition of Kohlberg and Mertens, but, rather than working with perturbations of the payoffs or strategy space, works directly with perturbations to the best reply correspondence. With the appropriate topology on this space of perturbations, the resulting definition does satisfy all of the requirements given by Kohlberg and Mertens. It is shown that one does not have much freedom in the topology one uses. Copyright 1990 by The Econometric Society.

Suggested Citation

  • Hillas, John, 1990. "On the Definition of the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 58(6), pages 1365-1390, November.
  • Handle: RePEc:ecm:emetrp:v:58:y:1990:i:6:p:1365-90
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    Cited by:

    1. Meroni, Claudia & Pimienta, Carlos, 2017. "The structure of Nash equilibria in Poisson games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 128-144.
    2. Zhe Yang & Yong Pu, 2013. "On existence and essential components for solution set for system of strong vector quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 55(2), pages 253-259, February.
    3. Anesi, Vincent, 2010. "Noncooperative foundations of stable sets in voting games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 488-493, November.
    4. repec:spr:topjnl:v:25:y:2017:i:2:d:10.1007_s11750-017-0447-2 is not listed on IDEAS
    5. Bajoori, Elnaz & Flesch, János & Vermeulen, Dries, 2013. "Perfect equilibrium in games with compact action spaces," Games and Economic Behavior, Elsevier, vol. 82(C), pages 490-502.
    6. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2015. "The refined best-response correspondence in normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 165-193, February.
    7. Srihari Govindan & Robert Wilson, 2008. "Metastable Equilibria," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 787-820, November.
    8. Swinkels Jeroen M., 1993. "Adjustment Dynamics and Rational Play in Games," Games and Economic Behavior, Elsevier, vol. 5(3), pages 455-484, July.
    9. Vermeulen, A. J. & Jansen, M. J. M., 2001. "An ordinal selection of stable sets in the sense of Hillas," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 161-167, November.
    10. Sofía Correa & Juan Torres-Martínez, 2014. "Essential equilibria of large generalized games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 479-513, November.
    11. Vermeulen, Dries & Jansen, Mathijs, 2005. "On the computation of stable sets for bimatrix games," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 735-763, September.
    12. Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
    13. Carlos Pimienta, 2014. "Bayesian and consistent assessments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 601-617, April.
    14. Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.
    15. Vermeulen, A. J. & Jansen, M. J. M., 1997. "On the invariance of solutions of finite games," Mathematical Social Sciences, Elsevier, vol. 33(3), pages 251-267, June.
    16. Jeroen Kuipers & Dries Vermeulen & Mark Voorneveld, 2010. "A generalization of the Shapley–Ichiishi result," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 585-602, October.
    17. De Sinopoli, Francesco & Meroni, Claudia & Pimienta, Carlos, 2014. "Strategic stability in Poisson games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 46-63.
    18. Mario Gilli, 2002. "Iterated Admissibility as Solution Concept in Game Theory," Working Papers 47, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
    19. Battalio,R. & Samuelson,L. & Huyck,J. van, 1998. "Risk dominance, payoff dominance and probabilistic choice learning," Working papers 2, Wisconsin Madison - Social Systems.
    20. Hauk, Esther & Hurkens, Sjaak, 2002. "On Forward Induction and Evolutionary and Strategic Stability," Journal of Economic Theory, Elsevier, vol. 106(1), pages 66-90, September.
    21. Kim, Sung H., 1997. "Continuous Nash equilibria," Journal of Mathematical Economics, Elsevier, vol. 28(1), pages 69-84, August.
    22. Keyzer, Michiel & van Wesenbeeck, Lia, 2005. "Equilibrium selection in games: the mollifier method," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 285-301, April.
    23. Man, Priscilla T.Y., 2012. "Efficiency and stochastic stability in normal form games," Games and Economic Behavior, Elsevier, vol. 76(1), pages 272-284.

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